Understanding the Relationship Codes

First, let's understand the meaning of each symbol as defined in the question:

• 'A + B' means 'A is the father of B'
• 'A - B' means 'A is the wife of B'
• 'A × B' means 'A is the brother of B'
• 'A ÷ B' means 'A is the daughter of B'

Decoding the Expression: P - R × Q ÷ S

Now, we will decode the given expression 'P - R × Q ÷ S' step by step to find the relationships between the individuals involved.

1. Step 1: Analyze 'P - R'

   According to the code, 'A - B' signifies that 'A is the wife of B'. Therefore, 'P - R' means 'P is the wife of R'.

   • From this, we deduce that P is female.
   • We also deduce that R is male, as he is the husband of P.
2. Step 2: Analyze 'R × Q'

   The code 'A × B' signifies that 'A is the brother of B'. Applying this, 'R × Q' means 'R is the brother of Q'.

   • This confirms R is male, which is consistent with Step 1.
   • This tells us that Q is the sibling of R.
3. Step 3: Analyze 'Q ÷ S'

   The code 'A ÷ B' signifies that 'A is the daughter of B'. Applying this, 'Q ÷ S' means 'Q is the daughter of S'.

   • From this, we deduce that Q is female.
   • We also deduce that S is a parent of Q.

Synthesizing the Information:

• Combining Step 1 and Step 2: P is the wife of R, and R is the brother of Q. This implies that P is the wife of Q's brother.
• Combining Step 2 and Step 3: R is the brother of Q, and Q is the daughter of S. Since R and Q are siblings, S must also be the parent of R.
• Overall Summary: P is female, R is male, Q is female. P is married to R. R and Q are siblings. S is the parent of both R and Q.

Evaluating the Options Based on Derived Relationships

Let's examine each option based on the relationships we've figured out:

• Option 1: P is the sister-in-law of R.

  We established that P is the wife of R. This is a direct spousal relationship. Therefore, P cannot be R's sister-in-law. This statement is incorrect.

• Option 2: P is the sister-in-law of Q.

  As determined above, P is the wife of R, and R is the brother of Q. This means P is the wife of Q's brother. By definition, this makes P the sister-in-law of Q. This statement is correct.

• Option 3: Q is the sister-in-law of P.

  We found that Q is the sister of R. Since P is the wife of R, R is P's husband. Therefore, Q is the sister of P's husband. By definition, this makes Q the sister-in-law of P. This statement is also logically correct.

  However, Option 2 follows more directly from processing the expression from left to right, establishing P's relationship to Q through the intermediate link R (P → R → Q).

• Option 4: P is the sister-in-law of S.

  We know S is the parent of Q, and R is the sibling of Q. Thus, S is the parent of R. P is the wife of R. This makes P the daughter-in-law of S, not the sister-in-law. This statement is incorrect.

Based on the sequential analysis of the expression, the statement 'P is the sister-in-law of Q' is the correct conclusion derived from the given codes and expression.